Re: OPs in the class M

[thk (Tom H. Koornwinder)]

I forward a next message from Thomas Dehn to OP-SF NET.
It is an addition and slight correction of his earlier comment
to Paul Nevai's posting to opsftalk.

		Tom Koorwinder
---------------------------------------------------------

Tom Koornwinder forwarded my following message
to OP-SF NET. I'd like to include
one correction and a little bit of
additional information:
 
 
 
> > Topic #3   -------------   OP-SF NET 5.2  ------------  March 15, 1998
> >                            ~~~~~~~~~~~~~
> > From: OP-SF NET  Editor <muldoon@yorku.ca>
> > Subject: From opsftalk
> >
> > Recent enquiries in opsftalk include the following query from Paul Nevai:
> >
> > "Is this new (I hope)?  If the measure is in the class M then there are
> > finitely many masspoints greater than 1 if and only if the ratio of the
> > consecutive ops evaluated at the point 1 converges to 1."
> 
> If I don't miss something (I work in a different area right
> now), I proved the above result in 1991, and it is contained
> both in my PhD thesis (which is written in German)
> and in my paper "A shortcut to asymptotics for
> orthogonal polynomials" (Theorem 8 in section 4.1 and
 
Correction: This is Theorem 4.3 (Sorry, I forgot to
check whether the numbering of theorems in the
printed version was the same as that in my TeX-file)
 
 
> the remark after the proof).
> published in J. Comp. and Appl. Math. in 1994.
 
It is in Volume 50, pages 207-219.
 
 
Hope this helps.
 
 
Thomas

Thomas Dehn
dehn@ipmsun5.mathematik.uni-karlsruhe.de
or
thomas.dehn@bgr.de (will be invalid after Jul 31st 1998).